Bipartite or two-mode networks are composed of two types of nodes, which we call agents and artifacts, and edges between nodes of one type and nodes of the other type. They can be used to represent a wide range of phenomena and therefore are studied in a diverse range of disciplines. For example, natural selection unfolds as species (the agents) compete over sites (the artifacts), commerce is possible as traders exchange resources, scientific advances are reported as scholars write papers, and laws are adopted as legislators sponsor bills. Although bipartite networks are useful in their own right, they can also be useful for inferring unipartite (i.e., one-mode) networks that would otherwise be difficult or impossible to measure directly. A bipartite projection transforms a bipartite network into a unipartite co-occurrence network in which agents are connected to the extent that they share artifacts. For example, competitive interaction networks can be inferred from species' co-occurrence in sites,[1]} trade networks can be inferred from firm co-location[2]} or product co-exchange,[3]} scholarly collaboration networks can be inferred from paper co-authorship,[4]} and political alliance networks can be inferred from bill co-sponsorship.[5]} Throughout the paper we use these applications to offer concrete examples, however the models we discuss are perfectly general and can be applied to derive unipartite backbones in a range of contexts.[6]}, [7]}, [8]} Indeed, in principle any unipartite network can be represented as the projection of some bipartite network.[9]}, [10]}, [11]}
